Manually ejecting a ball shouldn't be a problem.

Check your manual for how to access the switch test and make sure that all three trough switches are registering. While you're in there check that the lock switches register too.

"Free play button" do you mean you have an added button do give credits? Check the coin switches and this button in switch test as well

It's possible you may have a switch matrix issue as it sounds like many switches aren't working.... You might also want to reseat the switch matrix connectors 2J2 and 2J3 and the inline connector that goes from the head to the body from them

Definitely check the coin door switches. The left one is on the same column as the shooter lane switch. If the little trip wire is all boogered up it can short the coin switch to the door and if that happens the game will think a ball is sitting in the shooter lane and it will not kick out a ball.

Actually check /all/ the switches. Mine wouldn't start a few weeks back and it was because a ball had jammed a switch closed. When I freed up the stuck switch, it started. I don't know why the game is so finicky, but it is.